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Now that, hopefully, everyone has calmed down a bit, I have made some changes to my problematic question (http://mathoverflow.net/questions/14162/finite-versus-infinite-on-non-hausdorff-topologies-closed) and am wondering if people could take a look at it to see if it now makes more sense (and satisfies MO criteria for a reasonable question).
I should like to add that I'm surprised a bit at the reactions I got over my definition of a Hausdorff topology. It seems odd that no one caught the fact that it was simply a typo on my part (substituting $\ne$ for = by accident), though this assumes that my current definition is correct.
Thank you.
The question surely makes sense. I do not think it is very appropriate for MO, since it is asking for an example that should have come up in a general topology course so it is not quite a "research level math question".
I think that the definition of the Hausdorff property is really not needed---as essentially everyone on the site should know it!---and that the example is an extraordinarily elaborate example, involving concepts several orders of magnitude more complicated, than what it is (as far as I can see) supposed to exemplify.
Well, I will admit to being entirely self-taught in the area of topology and thus am not as familiar with examples of the sort I am seeking and I'll be perfectly content if someone here on meta simply gives me an example or a reference.
Edit: Which it appears someone did just as I posted this reply. Muchas gracias.
Well, you've got me there. Apparently Zev did notice it was a typo and I seemed to miss that. Nevertheless it seemed like a rather big "to-do" when someone could simply have changed the typo.
That said, I will note that there are questions on here that are basic undergraduate probability questions but no one seems to knock them. There seems to be an assumption that all the folks on this site have the same sort of background.
I guess I didn't read Pete's comments as saying he thought it was a typo. I thought I was defending the correct definition (which I obviously wasn't - sometimes no matter how many times one looks at something, if they're tired enough they won't see the error right in front of their face).
@Herr Dr. Pete: note that it is actually possible to obtain a BS in Mathematics from MIT without taking a formal course in topology: http://www-math.mit.edu/academics/undergrad/major/. Nevertheless, I will make sure I mention your concerns to the head of our math department since we don't require a full course in it (and before anyone says anything, I should note our math and physics graduates are presently at places like Yale, Dartmouth, Tufts, Boston College, etc.).
I am very pleased that you think there is a serious deficit in knowledge of probability theory among many mathematicians. It is a pet peeve of one of my colleagues in our math department and we were just talking about it yesterday.
In any case, while not an example from probability, here is a question that I thought was at an undergraduate level (since I taught this question and the given answer in a class a few years ago) that didn't get knocked down. I didn't knock it down because I didn't assume the person asking had had a background in the material:
http://mathoverflow.net/questions/14980/hat-problem-hamming-codes
The mathematics major at MIT has a few subdivisions, and the theoretical option does in fact require our topology course. I should add that one big reason not to require the topology course of non-theoretical math majors is that here a math / computer science double is much more common than a math / physics double, which is why the applied option has a strong emphasis on discrete math. (Also, the topology course is regarded as difficult - it's taught about half the time by Munkres, who has a very take-no-prisoners attitude about the whole thing.)
As far as the Hamming code problem, you'll note that it only has one vote, so it isn't exactly a great question. Probably the OP should have thought about the problem a little more.
@Qiaochu: I think we should be careful in assuming that few votes implies not-greatness. It could just as well have few votes because few people on MO are interested (or are qualified to judge). This is not a comment on the Hamming code problem; I am making a general statement here. (I am not the one who voted it up, though.)
And apparently I'm not the only one who thinks there is room for debate on just how research-oriented a question is: http://tea.mathoverflow.net/discussion/216/stop-closing-probability-questions-if-you-dont-know-probability/
@QY: I never said the Hamming code problem was good. It was simply an example of a problem that I considered undergraduate-level that did not get closed and/or knocked into the negative numbers.
But we digress. This thread was to be about my question on Hausdorff topologies and how I could improve it. I will be happy to debate undergraduate education and what makes a good research-level question on another thread.
Ian, I didn't like your phrase "Herr Dr Pete". I assumed the idea was something like: "Herr Dr" is German, German means Nazi, the Nazis told people what to do, and Pete was telling you what to do. Step number two is pretty offensive.
Tell me I jumped to the wrong conclusion, and that will make me happier.
@Tom: my charitable reading was that it was a jibe at credential-waving, using the fact that the German conventions keep all titles cumulatively (IIRC), thus "Herr Doktor Professor Weierstrass", which to an anglophone ear sounds excessively stilted. Like Thaddeus Grommit, BA, MA, MD, etc. It doesn't read so badly, I think, in the context of the discussion between Ian and Pete on what is and isn't covered in graduate training; although I didn't particularly care for it as rhetoric, I didn't think it was a Godwin.
(I don't think the Germans accumulate titles like that. But “professor” and “doctor” are somewhat orthogonal concepts, with neither implying the other, so it kind of makes sense (if you care about such things) to include both. They don't pile on their undergraduate degrees, though. This entire comment is in parenthesis in order to be more easily ignored.)
( http://www.google.com/search?q=%22Herr+doktor+professor%22 )
Pete, I wasn't really expecting you to be offended, because I assumed you would have said so if you had been. People trying to be funny sometimes blur the concepts of German and Nazi. (This is particularly common in Britain, unfortunately.) If I were German I really wouldn't like this, but it's generally objectionable to everyone, really.
Anyway, Yemon's charitable reading may be right. Looking back at the various comments, it seems very plausible, and it's certainly a happier interpretation.
@Tom: Actually I don't really think I meant it either way (though my meaning was closer to Yemon's). It was a Mel Brooks-ism and was supposed to inject a little light-heartedness into things. I have never heard it interpreted in the way in which you are interpreting it and I'm middle-aged. The Nazis were atrocious butchers but not all Germans were Nazis (my wife's family, for instance, is German Jewish). In addition, that title is not exclusive to Germany and Austria (Switzerland and Liechtenstein both employ it I believe).
@Pete: I appreciate the respect, but you can return to calling me Ian. Whether you meant it or not, after our blow out, it comes off as patronizing.
Ian: OK, thanks for clarifying. I've heard too much of this type of "humour", which as I said is sadly prevalent here in the UK, probably more than elsewhere. Sorry to have been unnecessarily suspicious.
@fpqc: I got my PhD in Scotland but I was (very proudly) born and raised in Buffalo, New York.
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